Deep learning has been extensively utilized for modeling and analysis of fluid turbulence. One such application is the use of super-resolution (SR) algorithms to reconstruct small-scale structures from their large-scale counterparts for turbulent flows. To date, all SR algorithms have been supervised or require unpaired reference data at a high resolution for training. This renders the model inapplicable to practical fluid flow scenarios, in which the generation of a high-resolution ground truth by resolving all scales down to the Kolmogorov scale becomes prohibitive. Hence, it is imperative to develop physics-guided models that exploit the multiscale nature of turbulence. Considering SR as a state-estimation problem, we present a self-supervised workflow based on deep neural networks to reconstruct small-scale structures that are relevant to homogeneous isotropic turbulence. In addition to visual similarity, we assessed the quality of the obtained reconstruction using spectra, structure functions, and probability density functions of the gradients of velocity and a passive scalar. From the analysis, we infer that the outputs of the workflow are in statistical agreement with the ground truth, for which the training pipeline is agnostic. Insights into learnability, interpretability, and generality of the trained networks have been provided as well. The results of this study can be leveraged to devise techniques for the reconstruction of small-scale structures using large-eddy simulation data.